By corollary 2.2.2 in [1]} \((k/N)Y_{N-k, N}\xrightarrow{} 1\) . Hence
\(\frac{Y_{N-k, N}}{Y_{N-4k}} & = 4\frac{(k/N)Y_{N-k, N}}{(4k/N)Y_{N-4k}} \xrightarrow{} 4,\\\frac{Y_{N-2k, N}}{Y_{N-4k}} & = 2\frac{(2k/N)Y_{N-2k, N}}{(4k/N)Y_{N-4k}} \xrightarrow{} 2.\) 
